Asymptotics for the sum of three state Markov dependent random variables

IF 0.7 Q3 STATISTICS & PROBABILITY
Gabija Liaudanskait.e, V. vCekanavivcius
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引用次数: 1

Abstract

The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the aggregate claims distribution after $n\in \mathbb {N}$ periods. The accuracy of order $O(n^{-1})$ and $O(n^{-1/2})$ is obtained for the local and uniform norms, respectively. In a particular case, the accuracy of estimates in total variation and non-uniform estimates are shown to be at least of order $O(n^{-1})$. The characteristic function method is used. The results can be applied to estimate the probable loss of an insurer to optimize an insurance premium.
三态马尔可夫相关随机变量和的渐近性
研究了当索赔金额取决于被保险人的状态(健康、生病或死亡)并且索赔以马尔可夫链连接时的保险模型。将有符号复合泊松近似应用于$n\in \mathbb {n}$周期后的总索赔分布。得到了局部范数$O(n^{-1})$和一致范数$O(n^{-1/2})$的精度。在特殊情况下,总变差估计和非均匀估计的精度至少为O(n^{-1})$阶。采用特征函数法。结果可用于估计保险公司的可能损失,以优化保险费。
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来源期刊
Modern Stochastics-Theory and Applications
Modern Stochastics-Theory and Applications STATISTICS & PROBABILITY-
CiteScore
1.30
自引率
50.00%
发文量
0
审稿时长
10 weeks
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